A148434 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 1, 0), (0, 1, 0), (1, -1, 1), (1, 1, -1)}.

1, 1, 2, 5, 19, 64, 257, 941, 3968, 15839, 69664, 290521, 1300855, 5596851, 25518160, 112525866, 519180302, 2328488717, 10843870533, 49326788502, 231519411263, 1064731724495, 5027517994091, 23328822545899, 110730474917654, 517671974178514, 2467712838619944, 11608392697739886, 55540653135855440

Offset

0,3

Links

Table of n, a(n) for n=0..28.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A148432 A047116 A148433 * A341762 A341878 A062122

Adjacent sequences: A148431 A148432 A148433 * A148435 A148436 A148437

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved